This is the problem:

There are 100 prisoners in solitary cells. There's a central living room with one light bulb; this bulb is initially off. No prisoner can see the light bulb from his or her own cell. Everyday, the warden picks a prisoner equally at random, and that prisoner visits the living room. While there, the prisoner can toggle the bulb if he or she wishes. Also, the prisoner has the option of asserting that all 100 prisoners have been to the living room by now. If this assertion is false, all 100 prisoners are shot. However, if it is indeed true, all prisoners are set free and inducted into MENSA, since the world could always use more smart people. Thus, the assertion should only be made if the prisoner is 100% certain of its validity. The prisoners are allowed to get together one night in the courtyard, to discuss a plan. What plan should they agree on, so that eventually, someone will make a correct assertion?

I have seen this problem on othe forums, and here are some of the best solutions (to my opinion):

1) At the beginning, the prisoners select a leader. Whenever a person (with the exeption of the leader) comes into a room, he turns the lights on. If the lights are already on, he does nothing. When the leader goes into the room, he turns off the lights. When he will have turned off the lights 99 times, he is 100% sure that everyone has been in the room.

2)wait 3 years, and with a great probability say that everyone has been in the room.

Does anyone know The optimal solution???

I have taken this problem from the www.ocf.berkeley.edu site, but I believe that you can find it on many others.